He 2++ molecular ion in a strong time-dependent magnetic field: a current-density functional study

The He molecular ion exposed to a strong ultrashort time‐dependent (TD) magnetic field of the order of 10⁹ G is investigated through a quantum fluid dynamics (QFD) and current‐density functional theory (CDFT) based approach using vector exchange‐correlation (XC) potential and energy density functional that depend not only on the electronic charge‐density but also on the current density. The TD‐QFD‐CDFT computations are performed in a parallel internuclear‐axis and magnetic field‐axis configuration at the field‐free equilibrium internuclear separation R = 1.3 au with the field‐strength varying between 0 and 10¹¹ G. The TD behavior of the exchange‐ and correlation energy of the He is analyzed and compared with that obtained using a [B‐TD‐QFD‐density functional theory (DFT)] approach based on the conventional TD‐DFT under similar computational constraints but using only scalar XC potential and energy density functional dependent on the electronic charge‐density alone. The CDFT based approach yields TD exchange‐ and correlation energy and TD electronic charge‐density significantly different from that obtained using the conventional TD‐DFT based approach, particularly, at typical magnetic field strengths and during a typical time period of the TD field. This peculiar behavior of the CDFT‐based approach is traced to the TD current‐density dependent vector XC potential, which can induce nonadiabatic effects causing retardation of the oscillating electronic charge density. Such dissipative electron dynamics of the He molecular ion is elucidated by treating electronic charge density as an electron‐“fluid” in the terminology of QFD. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Spherical‐harmonics expansion method for density‐matrix simulations of quantum electron dynamics in continuum states

Spherical‐harmonics expansion method is proposed to solve the quantum time‐evolution equations for density matrices numerically in momentum space. This method facilitates efficient real‐time simulations of quantum electron dynamics in continuum states through extension of our previous formalism developed for discrete states. Numerical accuracy and efficiency are demonstrated through two examples: (i) multiphoton ionization of a one‐electron atom in intense laser field, and (ii) real‐time dynamics of plasma oscillations in electron liquids. In case (i), coupled dynamics of density matrices for bound and continuum states reveals an enhancement of multiphoton ionization over the Keldysh approximation through resonant intermediate states. © 2015 Wiley Periodicals, Inc.     

Effective potential energy curves of H2 molecule evolving in a strong time‐dependent magnetic field

Evolution of hydrogen molecule, starting initially from its field‐free ground state, in a time‐dependent (TD) magnetic field of order 10¹¹ G is presented in a parallel internuclear axis and magnetic field‐axis configuration. Effective potential energy curves (EPECs), in terms of exchange and correlation energy, of the hydrogen molecule as a function of TD magnetic‐field strength, are analyzed through TD density functional computations based on a quantum fluid dynamics approach. The numerical computations are performed for internuclear separation R ranging from 0.1 to 14.0 a.u. The EPECs exhibit field‐dependent significant potential‐well minima both at large internuclear separations and at short internuclear separations with a considerable increase in the exchange and correlation energy of the hydrogen molecule. The results, when compared with the time‐independent (TI) studies involving static TI magnetic fields, reveal TD behavior of field‐dependent crossovers between different spin‐states of hydrogen molecule as indicated by the TI investigations in static magnetic fields. Besides this, present work reveals interesting dynamics in the TD total‐electronic charge‐density distribution of the hydrogen molecule. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Quantum-chemical analysis of the CuCl2 molecule

This paper reports on quantum-chemical analysis of the linear structure of CuCl₂ by Hartree-Fock (HF) and density functional theory (DFT) methods and also by time-dependent HF (TD HF) and DFT (TD DFT) techniques. Using pure DFT exchange correlation functional (B3LYP) yields the best agreement with the experimental electronic spectra of CuCl₂. In this case, the odd electron is delocalized over the molecule, spin density on copper being 0.27. The ground state of the CuCl₂ molecule is ²Π_g with linear geometry.     

A numerical study of time-dependent schr?dinger equation for multiphoton vibrational interaction of NO molecule, modelled as Morse oscillator, with intense far-infrared femtosecond lasers

For the NO molecule, modelled as a Morse oscillator, time-dependent (TD) nuclear Schr?dinger equation has been numerically solved for the multiphoton vibrational dynamics of the molecule under a far-infrared laser of wavelength 10503 nm, and four different intensities,I = 1 × 10⁸, 1 × 10¹³, 5 × 10¹⁶, and 5 × 10¹⁸ W cm⁻² respectively. Starting from the vibrational ground state at zero time, various TD quantities such as the norm, dissociation probability, potential energy curve and dipole moment are examined. Rich high-harmonics generation (HHG) spectra and above-threshold dissociation (ATD) spectra, due to the multiphoton interaction of vibrational motions with the laser field, and consequent elevation to the vibrational continuum, have been obtained and analysed. Dedicated to Professor C N R Rao on his 70th birthday An erratum to this article is available at .     

Dynamics of electronic motion in hydrogen atom under parallel strong oscillating magnetic field and intense laser fields

The mechanism of ionization of an H atom interacting with intense laser electric fields is altered when a strong, oscillating magnetic field is applied along a direction parallel to the laser field. In this first study, these two strongly nonperturbative situations have been combined together and the corresponding time‐dependent (TD) Schrödinger equation has been numerically solved without using any basis set. The electric field arising out of the magnetic field and the magnetic field arising out of the laser electric field are found to be negligibly small, thereby not affecting the results. There are two main, apparently counter‐intuitive results from this study of parallel fields of the same frequency but different field strengths: (1) In presence of an oscillating magnetic field, the ionization rate due to the laser field diminishes, and (2) increasing the laser intensity, keeping the magnetic field strength the same, makes the electron density ionize with a lesser rate, in contrast to the situation with intense lasers in the absence of a strong TD magnetic field. © 2015 Wiley Periodicals, Inc.     

Time-dependent bond-current functional theory for lattice Hamiltonians: Fundamental theorem and application to electron transport

The cornerstone of time-dependent (TD) density functional theory (DFT), the Runge-Gross theorem, proves a one-to-one correspondence between TD potentials and TD densities of continuum Hamiltonians. In all practical implementations, however, the basis set is discrete and the system is effectively described by a lattice Hamiltonian. We point out the difficulties of generalizing the Runge-Gross proof to the discrete case and thereby endorse the recently proposed TD bond-current functional theory (BCFT) as a viable alternative. TDBCFT is based on a one-to-one correspondence between TD Peierl’s phases and TD bond-currents of lattice systems. We apply the TDBCFT formalism to electronic transport through a simple interacting device weakly coupled to two biased non-interacting leads. We employ Kohn-Sham Peierl’s phases which are discontinuous functions of the density, a crucial property to describe Coulomb blockade. As shown by explicit time propagations, the discontinuity may prevent the biased system from ever reaching a steady state.     

Stripped ion–helium atom collision dynamics within a time-dependent quantum fluid density functional theory

A nonperturbative, time-dependent (TD) quantum mechanical approach is described for studying the collision dynamics between the He atom and a fully stripped ion. The method combines quantum fluid dynamics and density functional theory to solve two coupled equations: one for the trajectory of the projectile nucleus and the other for the electronic charge distribution of the target atom. The computed TD and frequency-dependent properties provide detailed features of the collision process. Inelastic and ionization cross sections are also reported. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 251–271, 1998     

An open‐source framework for analyzing N‐electron dynamics. II. Hybrid density functional theory/configuration interaction methodology

In this contribution, we extend our framework for analyzing and visualizing correlated many‐electron dynamics to non‐variational, highly scalable electronic structure method. Specifically, an explicitly time‐dependent electronic wave packet is written as a linear combination of N‐electron wave functions at the configuration interaction singles (CIS) level, which are obtained from a reference time‐dependent density functional theory (TDDFT) calculation. The procedure is implemented in the open‐source Python program det CI@ORBKIT, which extends the capabilities of our recently published post‐processing toolbox (Hermann et al., J. Comput. Chem. 2016, 37, 1511). From the output of standard quantum chemistry packages using atom‐centered Gaussian‐type basis functions, the framework exploits the multideterminental structure of the hybrid TDDFT/CIS wave packet to compute fundamental one‐electron quantities such as difference electronic densities, transient electronic flux densities, and transition dipole moments. The hybrid scheme is benchmarked against wave function data for the laser‐driven state selective excitation in LiH. It is shown that all features of the electron dynamics are in good quantitative agreement with the higher‐level method provided a judicious choice of functional is made. Broadband excitation of a medium‐sized organic chromophore further demonstrates the scalability of the method. In addition, the time‐dependent flux densities unravel the mechanistic details of the simulated charge migration process at a glance. © 2017 Wiley Periodicals, Inc.     

Time-dependent density-functional studies of the D2 coulomb explosion

Real-time first principle simulations are presented of the D(2) Coulomb explosion dynamics detonated by exposure to very intense few-cycle laser pulse. Three approximate functionals within the time-dependent density functional theory (TDDFT) functionals are examined for describing the electron dynamics, including time-dependent Hartree-Fock theory. Nuclei are treated classically with quantum corrections. The calculated results are sensitive to the underlying electronic structure theory, showing too narrow kinetic energy distribution peaked at too high kinetic energy when compared with recent experimental results (Phys. Rev. Lett. 2003, 91, 093002). Experiment also shows a low energy peak which is not seen in the present calculation. We conclude that while Ehrenfest-adiabatic-TDDFT can qualitatively account for the dynamics, it requires further development, probably beyond the adiabatic approximation, to be quantitative.     

Time-dependent density-functional and reduced density-matrix methods for few electrons: Exact versus adiabatic approximations

To address the impact of electron correlations in the linear and non-linear response regimes of interacting many-electron systems exposed to time-dependent external fields, we study one-dimensional (1D) systems where the interacting problem is solved exactly by exploiting the mapping of the 1D N-electron problem onto an N-dimensional single electron problem. We analyze the performance of the recently derived 1D local density approximation as well as the exact-exchange orbital functional for those systems. We show that the interaction with an external resonant laser field shows Rabi oscillations which are detuned due to the lack of memory in adiabatic approximations. To investigate situations where static correlations play a role, we consider the time-evolution of the natural occupation numbers associated to the reduced one-body density matrix. Those studies shed light on the non-locality and time-dependence of the exchange and correlation functionals in time-dependent density and density-matrix functional theories.     

Real-time propagation of the reduced one-electron density matrix in atom-centered orbitals: application to multielectron dynamics of carbon clusters C(n) in the strong laser pulses

We present a time-dependent density functional theory (TDDFT) study on the electron dynamics of small carbon clusters C(n) (n = 9, 10) exposed to a linearly polarized (LP) or circularly polarized (CP) oscillating electric field of ultrafast laser with moderate laser intensity. The multielectron dynamics is described by propagating the reduced one-electron density matrix in real-time domain. The high harmonic generation (HHG) spectra of emission as well as the time evolution of atomic charges, dipole moments and dipole accelerations during harmonic generation are calculated. The microscopic structure-property correlation of carbon chains is characterized. It is found that the electron responses of C(n) to the laser field oscillation become nonadiabatic as the field intensity is larger than 1.4 x 10(13) W/cm(2). The nonadiabatic multielectron effect is displayed by an explicit fluctuation on the induced atomic charges and the instantaneous dipole acceleration and by observing the additional peaks other than those predicted from the spectral selection rule in HHG spectra of C(n) as well. The origin of these additional peaks is elucidated. The atomic charges of C(n) in LP and CP laser pulses experience different type of oscillations as expected. In the linear structure C9, the atomic charges at the two ends experience larger amplitude oscillations than those near the chain center whereas the induced charges on each atom of C10 experience the equal amplitude oscillations in the CP laser pulse.     

Time-dependent multiconfiguration theory for electronic dynamics of molecules in intense laser fields: a description in terms of numerical orbital functions

The equations of motion (EOMs) for spin orbitals in the coordinate representation are derived within the framework of the time-dependent multiconfiguration theory developed for electronic dynamics of molecules in intense laser fields. We then tailor the EOMs for diatomic (or linear) molecules to apply the theory to the electronic dynamics of a hydrogen molecule in an intense, near-infrared laser field. Numerical results are presented to demonstrate that the time-dependent numerical multiconfiguration wave function is able to describe the correlated electron motions as well as the ionization processes of a molecule in intense laser fields.     

Relaxation and dephasing in open quantum systems time-dependent density functional theory: Properties of exact functionals from an exactly-solvable model system

The dissipative dynamics of many-electron systems interacting with a thermal environment has remained a long-standing challenge within time-dependent density functional theory (TDDFT). Recently, the formal foundations of open quantum systems time-dependent density functional theory (OQS-TDDFT) within the master equation approach were established. It was proven that the exact time-dependent density of a many-electron open quantum system evolving under a master equation can be reproduced with a closed (unitarily evolving) and non-interacting Kohn-Sham system. This potentially offers a great advantage over previous approaches to OQS-TDDFT, since with suitable functionals one could obtain the dissipative open-systems dynamics by simply propagating a set of Kohn-Sham orbitals as in usual TDDFT. However, the properties and exact conditions of such open-systems functionals are largely unknown. In the present article, we examine a simple and exactly-solvable model open quantum system: one electron in a harmonic well evolving under the Lindblad master equation. We examine two different representitive limits of the Lindblad equation (relaxation and pure dephasing) and are able to deduce a number of properties of the exact OQS-TDDFT functional. Challenges associated with developing approximate functionals for many-electron open quantum systems are also discussed.     

Time‐Dependent Density Functional Theory Molecular Dynamics Simulations of Liquid Water Radiolysis

The early stages of the Coulomb explosion of a doubly ionized water molecule immersed in liquid water are investigated with time‐dependent density functional theory molecular dynamics (TD–DFT MD) simulations. Our aim is to verify that the double ionization of one target water molecule leads to the formation of atomic oxygen as a direct consequence of the Coulomb explosion of the molecule. To that end, we used TD–DFT MD simulations in which effective molecular orbitals are propagated in time. These molecular orbitals are constructed as a unitary transformation of maximally localized Wannier orbitals, and the ionization process was obtained by removing two electrons from the molecular orbitals with symmetry 1B₁, 3A₁, 1B₂ and 2A₁ in turn. We show that the doubly charged H₂O²⁺ molecule explodes into its three atomic fragments in less than 4 fs, which leads to the formation of one isolated oxygen atom whatever the ionized molecular orbital. This process is followed by the ultrafast transfer of an electron to the ionized molecule in the first femtosecond. A faster dissociation pattern can be observed when the electrons are removed from the molecular orbitals of the innermost shell. A Bader analysis of the charges carried by the molecules during the dissociation trajectories is also reported.     

Ultrafast Electron Transfer with Symmetrical Quasi-classical Dynamics based on Mapping Hamiltonian and Quantum Dynamics based on ML-MCTDH

Symmetrical quasi-classical (SQC) method based on mapping Hamiltonian is an efficient approach that is potentially useful to treat the nonadiabatic dynamics of very large systems. We try to evaluate the performance of this method in the ultrafast electron transfer processes involving a few of electronic states and a large number of vibrational modes. The multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) method was used to get the accurate dynamical results for benchmark. Although the population dynamics in the longtime limit show differences in the ML-MCTDH and SQC calculations, the SQC method gives acceptable results.     

Mechanisms of double ionization in strong laser field from simulation with Coupled Coherent States: Beyond reduced dimensionality models

The recently developed Coupled Coherent States method for solution of the time-dependent Schrödinger equation is used to simulate the strong laser field double ionization of a helium atom in six spatial dimensions. The calculated double ionization yield, as a function of laser intensity, reproduces the “shoulder”, attributable to electron recollisions. The method, which employs a Coherent State representation guided by classical trajectories also provides physical insight into the ionization mechanism. The appearance of the ‘shoulder’, is seen by analysis of the guiding trajectories to arise predominantly from sequential excitation of one electron into a highly excited orbit, followed by an electron–electron collision leading to correlated escape of the two electrons. A second little known mechanism involves recollisions resulting in ionization of the secondary electron, leaving the first in a highly excited state, from which it is later ionized by the laser field.     

Excited state properties of sizable molecules in solution: from structure to reactivity

We review some recent advances in quantum mechanical methods devised specifically for the study of excited electronic state of large size molecules in solution. The adopted theoretical/computational framework is rooted in the density functional theory (DFT) and its time-dependent extension (TD-DFT) for the characterization of ground and excited states, in the polarizable continuum model (PCM) for the treatment of bulk solvent effects, and in time-dependent quantum mechanical methods for chemical dynamics. Selected applications to the simulation of absorption spectra, to the interpretation of time-resolved experiments, and to the computation of dissociative electron transfer rates are presented and discussed.